Control And Stabilization Of Partial Differential Equations

Author : Iasson Karafyllis,Miroslav Krstic
Publisher : Springer
Page : 287 pages
File Size : 41,8 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319910116

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Input-to-State Stability for PDEs by Iasson Karafyllis,Miroslav Krstic Pdf

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Author : Kais Ammari
Publisher : SMF
Page : 119 pages
File Size : 42,6 Mb
Release : 2015-07-01
Category : Electronic
ISBN : 2856298176

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Control and Stabilization of Partial Differential Equations by Kais Ammari Pdf

Author : Aziz Belmiloudi
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 52,9 Mb
Release : 2008-08-17
Category : Technology & Engineering
ISBN : 9781848003446

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Stabilization, Optimal and Robust Control by Aziz Belmiloudi Pdf

Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.

Author : Miroslav Krstic,Andrey Smyshlyaev
Publisher : SIAM
Page : 197 pages
File Size : 50,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718607

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Boundary Control of PDEs by Miroslav Krstic,Andrey Smyshlyaev Pdf

The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.

Author : Ionuţ Munteanu
Publisher : Springer
Page : 214 pages
File Size : 43,6 Mb
Release : 2019-02-15
Category : Science
ISBN : 9783030110994

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Boundary Stabilization of Parabolic Equations by Ionuţ Munteanu Pdf

This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.

Author : Kaïs Ammari,Serge Nicaise
Publisher : Springer
Page : 178 pages
File Size : 50,5 Mb
Release : 2014-11-03
Category : Mathematics
ISBN : 9783319109008

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Stabilization of Elastic Systems by Collocated Feedback by Kaïs Ammari,Serge Nicaise Pdf

By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.

Author : Georges Bastin,Jean-Michel Coron
Publisher : Birkhäuser
Page : 307 pages
File Size : 54,7 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319320625

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Stability and Boundary Stabilization of 1-D Hyperbolic Systems by Georges Bastin,Jean-Michel Coron Pdf

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Author : Martin Gugat
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 2015
Category : Electronic
ISBN : 3319188917

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Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems by Martin Gugat Pdf

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

Author : Weijiu Liu
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 51,5 Mb
Release : 2009-12-01
Category : Mathematics
ISBN : 9783642046131

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Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation by Weijiu Liu Pdf

Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.

Author : Thomas Meurer
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 42,7 Mb
Release : 2012-08-13
Category : Technology & Engineering
ISBN : 9783642300158

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Control of Higher–Dimensional PDEs by Thomas Meurer Pdf

This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.

Author : Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels
Publisher : Springer
Page : 571 pages
File Size : 51,6 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319644899

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Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs by Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels Pdf

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

Author : Kaïs Ammari,Fathi Hassine
Publisher : Springer Nature
Page : 156 pages
File Size : 51,7 Mb
Release : 2022-09-20
Category : Mathematics
ISBN : 9783031125195

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Stabilization of Kelvin-Voigt Damped Systems by Kaïs Ammari,Fathi Hassine Pdf

This monograph examines the stability of various coupled systems with local Kelvin-Voigt damping. The development of this area is thoroughly reviewed along with the authors’ contributions. New results are featured on the fundamental properties of solutions of linear transmission evolution PDEs involving Kelvin-Voigt damping, with special emphasis on the asymptotic behavior of these solutions. The vibrations of transmission problems are highlighted as well, making this a valuable resource for those studying this active area of research. The book begins with a brief description of the abstract theory of linear evolution equations with a particular focus on semigroup theory. Different types of stability are also introduced along with their connection to resolvent estimates. After this foundation is established, different models are presented for uni-dimensional and multi-dimensional linear transmission evolution partial differential equations with Kelvin-Voigt damping. Stabilization of Kelvin-Voigt Damped Systems will be a useful reference for researchers in mechanics, particularly those interested in the study of control theory of PDEs.

Author : V.I. Vorotnikov
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461241508

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Partial Stability and Control by V.I. Vorotnikov Pdf

Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: • "Lotka-Volterra ecological principle of extinction;" • focusing and acceleration of particles in electromagnetic fields; • "drift" of the gyroscope axis; • stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.

Author : Viorel Barbu
Publisher : Springer
Page : 226 pages
File Size : 55,8 Mb
Release : 2018-04-26
Category : Science
ISBN : 9783319766669

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Controllability and Stabilization of Parabolic Equations by Viorel Barbu Pdf

This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.

Author : Jean-michel Coron,Tatsien Li,Zhiqiang Wang
Publisher : World Scientific
Page : 315 pages
File Size : 41,8 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9789811271649

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Control Of Partial Differential Equations by Jean-michel Coron,Tatsien Li,Zhiqiang Wang Pdf

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.